I assume you mean from Leon in Spain, not Lyon in France.
The Caminos have a great variety of surfaces--its one of the things that makes them so fun to ride.
One can ride a mountain bike on the paved road much more easily than riding a road (or hybrid) bike on a trail. If you have something other than a mountain bike you'll be on and off the marked trail quite a bit.
Leon is not too far, and I've seen plenty of hybrid type bikes ride much of it. You'll miss some great parts, but if you aren't into mountain biking you might be better off on the road when it gets rougher. If you are actually coming from Lyon, it would definitely be worth getting a nice bike.